I think the best answer is that there's no one answer.
Let's start with the easiest of your questions: you've read a biography of someone you've never met. Do you know them? Most people would say "No" because when we say things like "I know Robin," we generally mean that we are acquainted with Robin--have actually met Robin. Knowing about someone is knowledge by description but not by acquaintance, to borrow Bertrand Russell's terms.
In the other cases, there's no simple answer because the terms "mere acquaintance," "friend," "close friend" and so on aren't precise; there's no cut-off. It's like the case of baldness. There's no exact point at which a formerly hirsute person becomes unequivocally bald.* The case you've focused on is an instance of a very general phenomenon. Some people are definitely tall, some are not tall, and some are on the border. Some bananas are definitely ripe, some are not, and for some there's no definite right answer. As you can see, it would be easy to make a very...

As it turns out, we don't get paid. One reason is that, as you may have noticed, there's no charge to ask a question and there's no tip jar. ;-)
On to the question. It's an empirical question; it depends on how our minds and bodies actually work. But it's pretty safe to say that the answer is yes: sometimes you can tell things about a person by the look in their eyes. It's far from perfect and not always reliable, but there's no completely reliable way to know what a person's state of mind is, so that's not a special problem for this case.
In fact, there's not much mystery here from the point of view of common sense. Most of us are at least tolerably good at reading facial expressions. And as for the eyes, they're part of the expression. A fake smile won't give you crow's feet; a genuine smile raises the cheeks and makes the corners of the eyes crinkle. We can learn to tell the difference. That's just one example.
Of course, it's not always so simple. A person's facial expression (eyes especially) may...

I guess I'd have to disagree with the idea that "all of philosophy and logic point to a reason or cause for everything." There's certainly no argument from logic as such; it's perfectly consistent to say that some events are genuinely random. Some philosophers have held that there's a reason (not necessarily a cause in the physical sense, BTW) for everything, but the arguments are not very good.
On the other hand... quantum mechanics is a remarkably well-confirmed physical theory that, at least as standardly interpreted, gives us excellent reason to think that some things happen one way rather than another with no reason or cause for which way they turned out.
An example: suppose we send a photon (a quantum of light) through a polarizing filter pointed in the vertical direction. We let the photon travel to a second polarizing filter, oriented at 45 degrees to the vertical. Quantum theory as usually understood says that there's a 50% chance that the photon will pass this filter and a 50% chance that it...

There are two questions here: first, can Descartes' cogito be doubted—is it open to doubt that "I" exist? Second, more generally, is there anything that's not open to legitimate or reasonable or rational doubt? (What people are psychologically capable of doubting maybe another matter.)
On the first, may philosophers would say yes. Even if it's certain that there's thinking going on, it doesn't follow that there's some one or some thing doing the thinking. Consider the Buddhist/ Humean "no self" view. On that way of understanding things, there's no substantial self. There is, as the Humean might say, just a bundle of perceptions. "I think," on this account, is just a manner of speaking. We can't get from "there is thinking" to "I exist."
So maybe it's open to doubt that I exist. Is it open to doubt that there's thinking going on when it seems that there is? Maybe not, though I don't doubt that some clever philosopher could offer an interesting argument to the contrary. What else? Can it...

It's a good question and the answer seems pretty plausibly to be yes. The impression that people have of themselves can often be off the mark, and that can be shown by how they actually behave. Someone who thinks he's generous might really be stingy, always finding excuses not to contribute his fair share. Someone who thinks she's not very smart might actually have a lot of insight, as those who know her can plainly see. And on it goes. We're complicated beings. There's no reason a priori to think that the part of our minds that tries to make sense of ourselves overall is likely to be especially good at it. No doubt there are some things about ourselves that we're in a better position than others to know, but when it comes to the larger patterns and dispositions that go into making us who we are, disinterested outsiders may well be in a better position than we are to get things right.

I think the simplest answer is this: empiricists think beliefs about matters of fact should be grounded in empirical evidence; they don't think the evidence always has to be direct. I've never been to New Zealand, but I have a considerable amount of indirect empirical evidence that it exists. To take just one bit of that evidence: people whom I know to be otherwise reliable and honest tell me they've been there. On the other hand, I don't even have indirect evidence that Middle Earth exists. What I have is evidence for is that J. R. R. Tolkien wrote stories about a fictional place called Middle Earth, which neither he nor anyone else claimed was real. The (small) larger point is this: the one-word name of a view is not always the best way to figure out what the view actually comes to. Very few, if any, self-described empiricists have said that evidence always has to be direct to be relevant.

You say that love is an emotion, and in some sense we can grant that. But saying it suggests that love is a feeling , and that, in turn, suggests that it's like a warm sensation in one's tummy -- something that we can simply detect by introspection and that we can't (or can't easily) be wrong about. But it's more complicated than that. If I love someone, I can still have moments when I feel angry at them, for example. But my momentary anger -- a non-loving feeling -- isn't the same as not loving them. Love is, among other things, a complicated set of dispositions. Some of them are dispositions to feel a certain way in certain situations, and others are dispositions to behave in certain ways. I might be momentarily angry with my daughter, for example, but it might be true that if anything were to happen to her, I would be beside myself with grief. I might also be willing to make considerable sacrifices for her well-being. I might worry about her, take time to check up on her, and do all of this not...

If I read you correctly, your point is this: if you're prepared to assert P, you should be prepared to assert that you know that P. And the converse is even clearer: if you are willing to assert that you know that P, you're willing to assert that P is true. That's an interesting and important observation, but it doesn't show that the standard analysis of knowledge is circular. Suppose I'm prepared to assert that P. Do I actually know that P? That depends. Even if I'm prepared to make a sincere assertion -- and hence believe that P -- I might not really be justified or P might not actually be true. In either case, the classical analysis says, I don't actually know that P. The analysis of knowledge doesn't make any reference to what people are prepared to assert. On the contrary: it points out how there can be a gap between what we're prepared to assert and what we actually know. We could turn this into a slogan: saying it's so is saying you know, but that doesn't mean you do.

There are a couple of ways we might think about the questions you're raising. One is by trying to look for an Archimedean Point, so to speak, that provides some sort of absolute or incontrovertible answer. The other way is to look at how we actually think about these sort of things -- look from the inside. Since I have no Archimedean point available to me, I'll offer the latter sort of response. What we think does depend on what we've experienced, but even though my life is different from yours, we have lots of common ground to appeal to. Obvious sort of case: if you and I were both to look out my office window, then even though your experience is not just like mine, we'd agree that there's a building directly across from us. We'd also agree that there's a large grassy area behind it, and that there are people wandering around in the vicinity. Other cases of ho-hum agreement among people are more complicated, but we could multiply examples indefinitely. We can also agree that some people are...